How to Solve Projectile Motion of a Stone Thrown at 30 Degrees Below Horizontal?

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SUMMARY

The projectile motion of a stone thrown at an angle of 30 degrees below the horizontal results in a time of flight of 1.57 seconds, an initial speed of 41.9 m/s, and an impact velocity of 51.2 m/s at an angle of -45 degrees with respect to the horizontal. The calculations utilize the equations for x-displacement and y-displacement, specifically x_final - x_initial = v_0 cos(theta) t and y_final - y_initial = v_0 sin(theta) t - 1/2 g t^2. The correct approach involves substituting the x-displacement to solve for the initial velocity in the y-displacement equation.

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Homework Statement



Suppose the stone is thrown at an angle of 30 degrees below the horizontal. If it strikes the ground 57m away. find (a) the time of flight (b) the initial speed, and (c) the speed and the angle of the velocity vector with respect to the horizontal at impact. (Hint: for part (a) use the equation for the x-displacement to eliminate volt from the equation for the y-displacement.)

answers: (a) 1.57s (b) 41.9 m/s (c) 51.2 m/s, -45 degrees

Homework Equations



x final- x inital= vo cos(theta)t
y final- y initial= vo sin(theta)t- 1/2g t^2

The Attempt at a Solution



i get that volt= 57/cos(30) and i plug it into the equation for y-position but i can't get the same answer.
 
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I'm a bit curious, what value are you using for the displacement y?
 

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